It all depends on the circumstances. I am pretty sure that - at least legally - there are situations where you'd be not punished for an act of revenge. (At least in Germany if you get hit, you can hit back - but you have to do it quickly! Otherwise it would count as a calculated and not as an emotional reaction.)
The appeal itself is mandatory because they have to bring the matter to the FA and push them. I am quite sure that they could make a case which would sound all to reasonable.
You're not talking about a "legal" issue here. This is not a person coming under an unprovoked or sustained assult or fearing for their lives. It was a bad tackle in a competative game of football. Something which happens all the time.
There are rules in football which every player knows and is aware they need to abide by. They're there to keep players safe, and also to protect football as a spectacle. The referee is there to run the game, not the players and he was rightly sent off for losing his temper. Those are the rules and they have been applied properly.
The last thing the FA will want is to give players any justification for behaving badly. There is no exception in the rule book and that's that. He should take his punishment, admit he lost his cool and move on. Any sort of softening by the FA will result in spurious appeals every other week when players aregue that they were provoked by name calling, or a bad tackle/off the ball incident twenty minutes earlier. It opens up a total can of worms.